Accuracy means how close a measurement comes to the true value while precision refers to how consistently one can repeat a measurement. Every measurement contains some uncertainty in them. It may be due to limitations in measurement tools, observer variation, or environmental factors. This affects both the accuracy and precision of measurements. In this article, we are going to learn about accuracy and precision in detail, along with their examples and differences.
Table of Content
Accuracy
Accuracy refers to how close a measurement is to the true value. It’s about being correct. In physics, accuracy refers to how close a measured value is to the true or accepted value of a physical quantity. For example, if a clock shows the time as 3:00 PM and it is 3:00 PM, the clock is accurate.
Accuracy measures how well the test or tool identifies or predicts the correct outcome. For example, if a thermometer reads 100 degrees and the actual temperature is 99.9 degrees, that thermometer is considered accurate.
Accuracy Formula
Accuracy is calculated using the following percent error formula:
Percent Error = {(Measured Value – True Value)/True Value} × 100
This formula gives us the accuracy as a percentage. The less the percent error the more accurate the value is.
Types of Accuracy
There are three ways to classify the accuracy of a system. They are :
- Point Accuracy
- Accuracy as Percentage of Scale Range
- Accuracy as Percentage of True Value
Point Accuracy
Point accuracy refers to how accurate an instrument is at a specific point on its scale. It does not reflect the overall accuracy of the instrument across its entire range. It only tells us how reliable the instrument is at that particular point.
Accuracy as Percentage of Scale Range
This type of accuracy is based on the uniformity of the instrument’s scale. For example, consider a thermometer with a scale up to 100 ℃. If this thermometer has an accuracy of ±0.5 per cent of the scale range, it translates to an error margin of ±0.5 ℃ (0.005 x 100 = ±0.5 ℃). This means any reading could be off by as much as 0.5 ℃.
Accuracy as Percentage of True Value
This measure of accuracy assesses how close the measured value is to the actual value. Instruments typically have an acceptable error margin, often around ±0.5 per cent from the true value. This standard helps in determining the precision of an instrument concerning what it is measuring.
Precision
Precision refers to how consistently a tool or process can produce similar results under the same conditions. It is about repeatability and reliability, not necessarily how close these results are to the true or intended value.
If we weigh something five times and each time the scale reads exactly 4.6 kg, our measurements are precise. They consistently show the same result.
Precision can be further broken down into two aspects:
- Repeatability
- Reproducibility
Repeatability
Repeatability refers to the variation in measurements taken by a single instrument or individual under unchanged conditions over a short period. For example, if we measure the length of a table several times in one sitting and get almost identical results each time, our measurements show good repeatability.
Reproducibility
Reproducibility is a measure of whether a measurement can be duplicated by different people, using different instruments, over extended periods. For example, if several different workers use different tape measures to size the same table on different days and their measurements are very close, the method is reproducible.
Precision Formula
To calculate precision, we use the formula for standard deviation, which shows how much the values in a set deviate from the average. Its formula is given by :
Standard Deviation (Precision) = √(∑(Measurement −Mean)2/ Number of measurements)
A smaller standard deviation indicates that the measurements are closely clustered around the mean, which means higher precision.
Accuracy and Precision Examples
Accuracy and precision are two fundamental concepts in measurement that can be illustrated with everyday examples.
Accuracy Examples
- If a weather forecast predicts a high of 75°F and the actual temperature is 75°F, the forecast is accurate. Accuracy in weather forecasting is crucial for planning and preparedness.
- When a recipe requires 1 teaspoon of salt, and you use a measuring spoon to add exactly 1 teaspoon, our measurement is accurate. Accurate measurements in cooking ensure the dish tastes as intended.
Precision Examples
- Imagine a bowler hits the same spot in the pins setup with every throw, regardless of strikes. This shows precision. The bowler’s throws are consistently hitting the same area, showing high precision in their aim and throw technique.
- In a factory, a machine that cuts pieces of metal to a length of 5.00 cm with very little variation among the pieces demonstrates precision. The ability to reproduce the same measurement consistently is critical for product quality.
Accuracy and Precision Combined Examples
- A diagnostic test that consistently and correctly identifies a condition without errors shows both accuracy and precision. Accurate and precise medical tests are vital for correct diagnosis and treatment.
- An archer who consistently hits the bullseye demonstrates both precision (hitting the same spot repeatedly) and accuracy (hitting the target spot).
Difference between Accuracy and Precision
Accuracy and precision are two distinct concepts in measurement. Here is the difference between accuracy and precision :
|
Accuracy vs. Precision |
||
|---|---|---|
| Aspect | Accuracy | Precision |
| Definition | The closeness of a measured value to a standard or known value. | The closeness of two or more measurements to each other. |
| Focus | Correctness of measurement relative to the true value. | Consistency of measurement results under the same conditions. |
| Dependence | Accuracy is dependent on the true value. | Precision is independent of accuracy and the true value. |
| Example | If a scale shows your weight as exactly what it truly is, it’s accurate. | If a scale shows the same weight every time you use it, it’s precise. |
| Illustration | Throwing darts that all land on the bullseye. | Throwing darts that land close to each other but not near the bullseye. |
| Measurement Error | Error describes how far a measurement is from the true value. | Error describes how spread out repeated measurements are. |
| Quality Indicator | Indicates how close a measurement is to the correct value. | Indicates how repeatable measurements are, regardless of accuracy. |
Also, Check
Solved Examples of Accuracy and Precision
Examples 1: A chemist measures the boiling point of water five times in a laboratory setting. The results are as follows: 99.8°C, 100.1°C, 100.0°C, 99.9°C, and 100.2°C. Knowing that the actual boiling point of water at sea level is exactly 100°C, calculate the accuracy and describe the precision of the measurements.
Solution :
- Accuracy: The average of the measurements is calculated by adding all the results together and dividing by the number of measurements:
Average = (99.8 + 100.1 + 100.0 + 99.9 + 100.2) /5 = 100.0°C
This average exactly matches the known boiling point of water, showing that the measurements are highly accurate. Accuracy here reflects how close the measurements are to the true or accepted value.
- Precision: Precision relates to the repeatability of measurements and how close the series of results are to each other. The range of measurements from 99.8°C to 100.2°C shows very tight clustering around the average. This indicates that the chemist’s measurements are consistently precise..
Examples 2: An archer practices by shooting arrows at a target, aiming for the bullseye. The scores recorded are 9, 10, 10, 9, 10. If 10 is the bullseye, assess the accuracy and precision of the archer’s shots.
Solution:
- Accuracy: Most of the archer’s shots hit the bullseye or very close to it, showing a high level of accuracy. Accuracy in this context is how close each shot is to the intended target, which is the bullseye.
- Precision: The shots consistently hit near or at the same spot (bullseye and just around it), indicating a high degree of precision. Precision here demonstrates the archer’s ability to deliver repeatable performance over multiple attempts.
Examples 3: A medical thermometer is calibrated to verify its accuracy at a known temperature of 37.0°C. It records the following temperatures: 36.8°C, 36.9°C, 37.1°C, 37.0°C, and 37.1°C. Evaluate the thermometer’s accuracy and precision based on these readings.
Solution:
Accuracy: The average reading is calculated as follows:
(36.8 + 36.9 + 37.1 + 37.0 + 37.1) /5 = 37.0°C
The average matches the expected temperature. This shows that the thermometer is accurate in measuring temperature.
Precision: The measurements are all within 0.3°C of each other, indicating a high level of precision. This demonstrates the thermometer’s ability to provide consistent results under the same conditions.
Examples 4: A machine in a factory is set to cut sheets of metal to a precise length of 200 cm. After production, five sheets are measured and found to be 200.1 cm, 199.8 cm, 200.0 cm, 200.2 cm, and 199.9 cm. Determine the machine’s accuracy and precision from these measurements.
Solution:
Accuracy: To find the average length:
(200.1+199.8+200.0+200.2+199.9) /5 =200.0cm
The average length exactly meets the specified length, demonstrating the machine’s accuracy in cutting the metal sheets.
Precision: The spread between the measurements is minimal, only varying by 0.4 cm, which signifies a high precision. This consistency shows that the machine can reliably reproduce the same length in its cuts.
Practice Questions on Accuracy and Precision
Q1: A student experiment measured to measure the acceleration due to gravity using a pendulum. The true value of gravity is approximately 9.81 m/s². The student records five measurements: 9.78 m/s², 9.79 m/s², 9.77 m/s², 9.79 m/s², and 9.78 m/s². Are these measurements accurate, precise, both, or neither? Explain your answer.
Q2: You have three thermometers. Each was used to measure the temperature of boiling water. The temperatures recorded were:
Thermometer A: 100°C, 100°C, 101°C
Thermometer B: 98°C, 98°C, 98°C
Thermometer C: 95°C, 100°C, 105°C Which thermometer is the most accurate? Which is the most precise?
Q3: In a physics lab, students use a ruler to measure the length of a metal rod. The actual length of the rod is 20.0 cm. Each student records their measurement. Student 1 records 20.0 cm, student 2 records 19.8 cm, and student 3 records 20.2 cm. Discuss the accuracy and precision of these measurements.
Q4: Explain how you would increase both the accuracy and precision of an experiment designed to measure the speed of sound in air using a standard stopwatch and two microphones spaced a known distance apart.
Q5: A group of students measured the period of a simple pendulum multiple times to calculate the gravitational constant. Their measurements show little variation between them, but the calculated value for gravity is significantly different from the accepted value of 9.81 m/s². Discuss potential reasons for the high precision but low accuracy of their results.
FAQs on Accuracy and Precision in Measurement
What is the difference between accuracy and precision in measurements?
Accuracy refers to how close a measurement is to the true value, while precision indicates how consistently you can get the same measurement under the same conditions.
Why is accuracy important in measurements?
Accuracy is crucial because it ensures that measurements reflect the true value as closely as possible, which is vital for valid data analysis, quality control, and decision-making.
Can measurements be precise but not accurate?
Yes, measurements can be precise but not accurate if they are consistently close to each other but far from the true value. This often happens due to systematic errors.
How can I improve the accuracy of my measurements?
To improve accuracy, calibrate your instruments regularly, follow standardized procedures, and eliminate any known biases in the measurement process.
What role does precision play in scientific measurements?
Precision is important in scientific measurements because it allows researchers to be confident in their results’ reproducibility, which is key for verifying experiments and theories.
How do I check the precision of a measurement tool?
Check the precision of a measurement tool by taking multiple measurements under the same conditions and observing how close these results are to one another.